@article{Banh Duc Dung_2012, title={THE RING WHOSE MODULE CLASS IS EMBEDDED IN PROJECTIVE MODULE}, volume={2}, url={https://jshe.ued.udn.vn/index.php/jshe/article/view/382}, DOI={10.47393/jshe.v2i2.382}, abstractNote={<p>Faith and Walker (1967) characterized QF rings as the class of rings if and if every right injective module is projective. It can be implied that if every right <em>R</em>-module is embedded in a projective module or, equivalently, in a free module, then <em>R</em> is QF. The question is if not all the module but a class of it is embedded, how the ring R is. The ring of which every finitely generated (cyclic) right <em>R</em>-module is embedded in a free module is called right FGF (resp. CF). There have been two conjectures:</p> <p>Right FGF ring is QF (FGF’s conjecture)?</p> <p>Right CF ring is artinian (CF’s conjecture)?</p> <p>If the CF’s conjecture is true, then so is FGF’s conjecture because a right artinian and FGF ring are QF. In this paper, we introduce these problems generally and then pose some open questions.</p>}, number={2}, journal={UED Journal of Social Sciences, Humanities and Education}, author={Banh Duc Dung}, year={2012}, month={Jun.}, pages={1-7} }